Mark Asta

Department of Chemical Engineering & Materials Science

Ab-Initio Molecular Dynamics Modeling of Molten Superalloys

ES09 Workshop University of California, Davis

June 25, 2009

Acknowledgements

Stefano Angioletti-Uberti1, Mike Finnis1, Peter Lee1, James Lill2, Dallas Trinkle3, Chris Woodward4

1Department of Materials, Imperial College London, UK 2High Performance Technologies Inc, WPAFB, Dayton, OH

3Department of Materials Science and Engineering, University of Illinois Urbana-Champaign

4Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base

Research Support US DOE (Office of Basic Energy Sciences)

AFOSR (Materials Engineering for Affordable New Systems Program)

Supercomputing Resources DoD ASC-MSRC Challenge Grant

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Evolution of Temperature Capability

Higher-T Materials Higher Efficiency

Ni-Based Superalloys

1st-Principles Thermo & Kinetic Modeling

• Design of High-Temperature Materials

–  Requires Data for Bulk and Interfacial Free Energies, Diffusion Kinetics, Lattice Parameters, … –  In Many Cases Data Difficult to Measure (e.g., Metastable Phases, High T)

• Role of 1st-Principles Calculations –  Predictive Framework for Computing Structural, Thermodynamic and Kinetic Properties –  Applicable to Both Stable and Metastable Phases, Bulk and

Interfaces, High & Low T

CMSX-4 Superalloy A.Dlouhy and G.Eggeler

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Ni62.936Cr7.5Mo0.38Al12.7Co9.9W2.1Ti1.3

Ta2.2Re0.95Hf0.034

Defects in Directional Solidification

Freckle Chain in Superalloy (Pollock and Murphy, 1996)

“Channels” in NH4Cl (Wooster, 1997)

Directionally Solidified Superalloy Ingot

(A. F. Giamei, UTRC)

Freckle-Formation Prediction

Convective Instabilities Expected When Critical Value of Ras Exceeded (e.g., Beckermann et al., 2000)

Channels in a Superalloy (Courtesy T. Pollock) Variation in Mass Density

Across Mushy Zone

Mushy Zone Permeability

Mushy Zone Height

Thermal Diffusivity and Viscosity

Ratio of Buoyancy to Retarding Frictional Forces

Gravity

Temperature Gradient

Low T

High T

Mass Density

Accurate Parametrization of Temperature and Composition Dependent Molar Volume and Solute Partitioning Required to

Predict Density Inversions Across Mushy Zone

• Assume Vα Depends Only on xα and T

–  Neglects Multicomponent Interactions

• Molar Volumes Fit to Experimentally Measured Binary Alloy Data

–  Large Variations of Partial Molar Volumes w/ Temperature & Composition Obtained from Fits

Molar-Volume Parametrization K. Mukai, Z. Li and K. C. Mills, Met. Trans. B, vol. 36B, 255 (2005)

Quantum MD for Molten Ni-Based Alloys

•  Simulation Details –  (NVT) Dynamics at T=1750 & 1830 K –  Time Step: 0.002 or 0.003 ps –  ~5-10 ps Simulation Time –  500 Atom System Size –  VASP Code on 64 Processors –  Ultrasoft Pseudopotentials and PAW

•  Volumes –  3 or 4 Volumes: 0.95 Vref – 1.05 Vref –  Equations of State and Equilibrium

Volume

•  Systems –  Elemental Ni and Al –  Binary Ni-Al, Ni-W, Ni-Re, Ni-Ta –  Ternary Ni-Al-W, Ni-Al-Re, Ni-Al-Ta

Snapshot of Simulation for Ni436Al50W14

Radial Distribution Functions •  Results Indicate Tendency for

Chemical Short-Range Ordering •  Nearest-Neighbor Bond Lengths RNiX < (RNiNi+RXX)/2

•  Nearest-Neighbor Coordinations gNiX(RNiX)>gNiNi(RNiNi)>gXX(RXX)

Liquid Structure Ni, Ni473W27 and Ni473Re27 at 1830 K

Liquid Structures Display Short Range Order Featuring Predominantly Icosahedral and BCC Local Structures

Bond Angle Distributions Common-Neighbor Analysis

Diffusion Constants

W Tracer Diffusion Constants Ni4W, 1830 K

Current Work

Ni-0.52 at.%W,1755-2022 K Leonard et al. (2004)

Pressure-Volume Relations Ni400Al100 at T=1830 K

T=1750 K T=1830 K

Composition Mukai AIMD VAIMD/VEXPT Mukai AIMD VAIMD/VEXPT

Ni500 7.4597 7.57(1) 1.015 7.5724 7.62(1) 1.006

Ni400Al100 7.7628 7.88(1) 1.015 7.8492 7.94(1) 1.012

Ni473W27 7.5534 7.66(1) 1.014 7.6520 7.70(1) 1.006

Ni400W100 6.5192 7.94(1) 7.3294 7.98(1)

Ni473Re27 7.4940 7.65(1) 7.6499 7.69(1)

Ni400Re100 7.5869 7.91(1) 7.8593 7.93(1)

Ni473Ta27 7.3310 7.70(1) 7.5053 7.75(1)

Ni400Ta100 1.1043 8.14(1) 4.1440 8.18(1)

Ni436Al50W14 7.6920 7.77(1) 7.7655 7.80(1)

Ni436Al50Re14 7.6921 7.7510 7.80(1)

Ni436Al50Ta14 7.6911 7.79(1) 7.7553 7.84(1)

All Volumes in Units of cm3/mole

Molar Volumes for Molten Ni-Based Alloys MD Calculations, Mukai Model and Experiment

Molar Volume Predictions Results for Ternary Ni-Al-W Alloys at T=1830 K

Ni Ni 4 Al Ni 436 Al 50 W 14 Ni 473 W 27 Ni

Model

MD Calculations

Ni

Ni 4 Al

Ni 473 W 27

Ni 436 Al 50 W 14

Ni

Ni 4 Al

Ni 473 W 27

Ni 436 Al 50 W 14

Ni

Ni 4 Al

Ni 473 W 27

Ni 436 Al 50 W 14

Similar results obtained for Ni-Al-Re and Ni-Al-Ta

Results suggest high accuracy of published parameterization for compositions bounded by experimental measurements

Ni-W T=1830 K

Ni-Re T=1830 K

Ni-Ta T=1830 K

Model

MD Calcs

Molar Volume Predictions Results for Binary Alloys

MD results demonstrate limitations in accuracy of published parameterizations when extrapolated beyond bounds of

experimental measurements

Partial Molar Volumes Results for Infinite Dilution

MD Calcs

Model

MD Calcs

Model

T=1830 K

T=1750 K

MD results suggest relatively weak temperature dependencies for partial molar volumes

Ni-W Ni-Re Ni-Ta

Ni-W Ni-Re Ni-Ta

Ab-Initio Calculations of Solid-Liquid Phase Equilibria Free Energies from “Perturbation” Approach

•  Free Energies Readily Derived for Classical Interatomic Potentials

– Thermodynamic Integration Employing MD and Monte-Carlo Methods

•  “Corrections” to Classical Free Energies to Achieve DFT Accuracy

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<…> Ensemble Average over States of Reference System A UB-UA Energy Difference Between System B and A for Given State of System A

S. Angioletti-Uberti, M. Asta, M. W. Finnis and P. D. Lee, Phys. Rev. B (2008) Closely related: C. W. Greeff, J. Chem. Phys. (2008)

Convergence Properties Description of Test System

•  Two classical Embedded Atom potentials for Ni-Cu –  Reference: “smf7” potential due to Foiles (1985) –  Target: “u3” potential due to Foiles, Baskes & Daw (1984)

•  Melting temperature and solidus/liquidus boundaries –  Known to be approximately 100 K higher for smf7 than u3 from

previous thermodynamic integration calculations

•  Compositions and trajectories –  Solid and Liquid Pure Ni: Reference trajectory from NVT MD –  Solid and Liquid NiCu Equiatomic Alloy: Reference

trajectory from NVT Monte-Carlo

•  Calculated quantities –  Free Energy Differences –  Differences in Pure-Ni Melting Temperatures

Convergence Properties Results for Test System

Convergence to within 1 meV/atom ~20 Steps for Pure Element

~100 Steps for Alloy

Convergence Properties Some Theoretical Considerations

Lu and Kofke (2001)

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exp(−βΔFtrue ) − exp(−βΔFcalc,B )exp(−βΔFtrue )

= PA (W )dW−∞

W0

∫

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Summary

•  Quantum molecular dynamics simulations of molten superalloys –  Good accuracy demonstrated for molar volumes, diffusivities (and

mixing enthalpies) –  Results provide data to refine molar-volume parametrizations for

higher length-scale models in materials design

•  Towards first-principles calculations of alloy solid-liquid phase equilibria and thermodynamic properties –  Free-energy perturbation approach as framework for coupling classical

and first-principles simulations for calculation of free energies with DFT accuracy

–  Promising convergence demonstrated for classical model system –  Approach requires reasonably accurate classical-potential models